Questions in differentiation

Select	Question
	The length of normal to the curve $x=a\,(\theta +\sin \theta ),$ $y=a(1-\cos \theta )$ at the point $\theta =\pi /2$ is
	The normal of the curve $x=a(\cos \theta +\theta \sin \theta )$ $y=a(\sin \theta -\theta \cos \theta )$ at any $\theta $ is such that
	The slope of the tangent to the curve $x=3{{t}^{2}}+1,y={{t}^{3}}-1$ at $x=1$ is
	An equation of the tangent to the curve $y={{x}^{4}}$ from the point (2, 0) not on the curve is
	The angle of intersection of the curves $y={{x}^{2}}$ and $x={{y}^{2}}$ at (1, 1) is
	The abscissae of the points, where the tangent to curve $y={{x}^{3}}-3{{x}^{2}}-9x+5$ is parallel to x-axis, are
	If the curve $y={{a}^{x}}$ and $y={{b}^{x}}$ intersect at angle $\alpha $ then,$\tan \alpha =$
	The equation of tangent at $(-4,\,-4)$ on the curve ${{x}^{2}}=-4y$ is
	The point at which the tangent to the curve $y=2{{x}^{2}}-x+1$ is parallel to $y\text{ }=\text{ 3}x+\text{9 }$ will be
	At what point on the curve ${{x}^{3}}-8{{a}^{2}}y=0$ , the slope of the normal is $\frac{-2}{3}$